The polar curve of a foliation on 2
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 849-863.

We study some properties of the polar curve P l associated to a singular holomorphic foliation on the complex projective plane 2 . We prove that, for a generic center l 2 , the curve P l is irreducible and its singular points are exactly the singular points of with vanishing linear part. We also obtain upper bounds for the algebraic multiplicities of the singularities of and for its number of radial singularities.

On étudie dans cet article quelques propriétés de la courbe polaire P l associée à un feuilletage holomorphe singulier dans le plan projectif complexe 2 . On démontre que, pour un centre l 2 générique, la courbe P l est irréductible et ses points singuliers sont précisément les points singuliers de avec partie linéaire nulle. On obtient aussi des bornes supérieurs pour la multiplicité algébrique des singularités de et pour son nombre de singularités radiales.

DOI: 10.5802/afst.1268
Mol, Rogério S. 1

1 Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627 C.P. 702, 30123-970 - Belo Horizonte - MG, BRAZIL
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Mol, Rogério S. The polar curve of a foliation on $\mathbb{P}^2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 849-863. doi : 10.5802/afst.1268. http://archive.numdam.org/articles/10.5802/afst.1268/

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